Reflection: High Quality Task Muddying the Waters: Formative Assessment Lesson  Section 3: Small Group Collaboration and Share Out
Student Work A: This is a case of a student clearly catching on to the flow of a discussion, without thinking for themselves. In the midst of a group or whole class discussion, I commonly tell my students not to "be puppets" and think for themselves. This student clearly understood the goal of the task without internalizing any reasons for her claims. Although she understood the overall idea, her reasoning was just as flawed as the statistics she was seeking to refute.
Student Work B: This is an exemplary response from a student who conveyed her ideas in writing very well. I really appreciated how she worded the second paragraph as "Not necessarily..." When teaching flaws in statistical analysis, students often jump the gun and try to refute everything that is not statistically sound thinking. It is important to recognize that even though the data collected is not sufficient enough to make a claim, it doesn't mean that the claim itself might not be true... It just can't be concluded from the data that was gathered. I shared this "Not necessarily" wording with the whole class on the following day. Excellent work!
Muddying the Waters: Formative Assessment Lesson
Lesson 21 of 21
Objective: SWBAT be active participants in a simulated study. SWBAT interpret data and evaluate statistical summaries. SWBAT critique some else's interpretation of data.
"Muddy the Waters"
This lesson is a formative assessment lesson that I have found on the Mathematics Assessment Project website. When I found it, I immediately could not wait to try it in my own classroom! As I read through the lessons, I was impressed with the critical thinking that was required, and I couldn't help but envision my students really getting into the role play skit. Throughout the course of this lesson, I have made adjustments to the template so that the activity can better fit my needs. I really wanted to fit it all in one class period, instead of dragging it out for 3 days  this is serving as the "grand finale" of my statistics unit, and is meant to be a one day celebration of what we have learned. Although the resources and framework are the same, I will be sure to make careful note of the things that I have changed in the lesson to adapt it to fit in a single day.
The lesson outline suggests teaching the activity in three lessons. However, I have converted "Lesson #1" to be my opening activity for this class period. Rather than sending the information home with the students the day before, I have elected to give it to them at the start of class. The opening activity gauges the students current skepticism of statistical usage. In this lesson we will work to teach the students to "put their filter on" when the consume statistics. Does correlation really imply causation? What claims are they making with the data? Is the data appropriate to use to make these claims?
When I first saw this lesson, I immediately appreciated how it was a lesson where the students could FEEL themselves grow  their initial responses will be a far cry from their ending conclusions!
Please refer to student handout (S1 and S2). Several of of "suggested questions" during the discussion are outstanding (page T4). Although I will not ask them all, a few that I will highlight and allow my students to discuss are the following:
 What does the chart show? What does the Riverside Manager say the chart shows? Is there a difference?
 If two things happen at the same time, does that mean one made the other happen?
 ADDITIONAL QUESTION: Does anyone have a story where one thing "appeared" to be the cause of an issue, but in reality the issue was much deeper?
 Does the way the question is asked make a ‘yes’ response more likely than ‘no’ or ‘maybe’? Why do you think that? Does it matter?

How could you rewrite the question in a more "unbiased" way?
Asking these questions is more than sufficient to get the students thinking critically. For the sake of time, I project these questions on a PowerPoint slide and ask the students to talk briefly with each other about each question before rejoining me for whole class share out (MP4).

Resources (2)
In this section of the lesson, I continue with the plan that is set forth in the template. Although it feels like the lesson is "rushing along" I am fully confident in my ability to fit the activities into a single day. The students will have more than enough time during this section of the lesson to share out. A key element to include if you are worried about the time, however, is an online stopwatch that is visible to the students. This keeps both, the teacher AND the students accountable!
At this time I also ask my students to respond to a poll question so that the results are streamed real time. This can be done through clickers, twitter, or my personal favorite... Poll Everywhere. It is great to display feedback from everyone in the class, and especially from students who are normally very reserved during a "share out" time.
Our discussion and collaborative activity takes up right up to the end of the period, (MP3), where I debrief with my students about what we have learned. I emphasize to them to keep an eye out as we progress through the class for flawed/misused statistics in the world around them. I even ask my students to bring in pictures, video clips, and newspapers that we can discuss as a class... these make for great "lesson launches" and bell ringers. Although we will soon me moving out of our statistics unit, we have only just begun to help our students establish their "mathematical filter" when they take in statistics from the world around them!
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